Reynolds-averaged stress and scalar-flux closures via symbolic regression for vertical natural convection

Abstract

Turbulent natural convection is characterised by mutual coupling effects between velocity and thermal fields. This inter-coupling induces simulation errors with linear and non-coupled turbulence closures commonly used in many Reynolds–averaged Navier–Stokes (RANS) approaches. In this paper, we re-examine the buoyancy-accounting algebraic scalar-flux model proposed by Kenjereš et al., Int. J. Heat Fluid Flow, Vol. 26, pp. 569–586 (2005). Using a term-by-term analysis on the model with the aid of high-fidelity datasets for natural convection flow between two differentially heated vertical plates, it is demonstrated that there are significant discrepancies in the predicted turbulent heat fluxes once the model is combined with the existing algebraic Reynolds stress models. As a result, we suggest including the quadratic terms in buoyancy-extended explicit algebraic Reynolds stress models, and have developed non-linear Reynolds-stress and heat-flux closure models via an in–house symbolic regression tool based on gene expression programming (GEP). The evaluation of these GEP-developed models shows significant improvements in the prediction of mean quantities and second-moments in an a priori stage and in an a posteriori stage, with the latter being realized by embedding the new models into the elliptic relaxation v2‾/k-f-k-ε-θ2‾ equations, for vertical natural convection with Rayleigh numbers in the range of 106 to 109.